Compound Direct Current (DC) Circuits - AP Physics 2

1. Find voltage if $I = 3 \text{A}$ and $R = 5 \text{Ω}$.

   $V = 15 \text{V}$. Apply Ohm's law: $V = 3 \times 5 = 15$.

2. What happens to total resistance when a resistor is added in parallel?

   Total resistance decreases. Parallel paths reduce overall resistance.

3. What is the formula for power using voltage and resistance?

   $P = \frac{V^2}{R}$. Derived from $P = VI$ and $I = \frac{V}{R}$.

4. What is the formula for power using current and resistance?

   $P = I^2R$. Derived from $P = VI$ and $V = IR$.

5. Calculate total resistance for $R_1 = 3 \text{Ω}$ and $R_2 = 6 \text{Ω}$ in parallel.

   $R_{\text{eq}} = 2 \text{Ω}$. $\frac{1}{R_{eq}} = \frac{1}{3} + \frac{1}{6} = \frac{1}{2}$.

6. What is Kirchhoff's Current Law?

   The total current entering a junction equals the total current leaving. Conservation of charge at circuit nodes.

7. Find power dissipated in a resistor if $I = 4 \text{A}$ and $R = 2 \text{Ω}$.

   $P = 32 \text{W}$. Use $P = I^2R = 4^2 \times 2 = 32$.

8. What is the formula for equivalent resistance in series?

   $R_{\text{eq}} = R_1 + R_2 + \text{...} + R_n$. Resistances add directly in series connections.

9. Calculate current if $Q = 10 \text{C}$ and $t = 5 \text{s}$.

   $I = 2 \text{A}$. Apply $I = \frac{Q}{t} = \frac{10}{5} = 2$.

10. Define electrical power in terms of voltage and current.

    $P = VI$. Power is the product of voltage and current.

11. What is the formula for voltage across a capacitor?

    $V = \frac{Q}{C}$. Voltage depends on stored charge and capacitance.

12. What is Kirchhoff's Voltage Law?

    The sum of EMFs equals the sum of voltage drops in a loop. Conservation of energy in closed loops.

13. What is the relationship between voltage, current, and resistance?

    Ohm's Law: $V = IR$. Fundamental relationship in electrical circuits.

14. What is the formula for equivalent resistance in parallel?

    $\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \text{...} + \frac{1}{R_n}$. Reciprocals add for parallel resistance calculations.

15. Calculate power if $I = 5 \text{A}$ and $R = 4 \text{Ω}$.

    $P = 100 \text{W}$. Use $P = I^2R = 5^2 \times 4 = 100$.

16. Find power if $V = 10 \text{V}$ and $I = 2 \text{A}$.

    $P = 20 \text{W}$. Power equals voltage times current: $10 \times 2$.

17. State the formula for electrical energy in terms of power and time.

    $E = Pt$. Energy equals power multiplied by time.

18. What happens to total resistance when a resistor is added in series?

    Total resistance increases. Series resistors add together.

19. Calculate total energy if $P = 60 \text{W}$ for $3 \text{h}$.

    $E = 648,000 \text{J}$. $E = 60 \times 10800 = 648,000$ J.

20. What is the principle of superposition in circuits?

    The voltage/current is the sum of individual contributions. Multiple sources combine linearly in circuit analysis.

21. Calculate total resistance for $R_1 = 4 \text{Ω}$ and $R_2 = 6 \text{Ω}$ in series.

    $R_{\text{eq}} = 10 \text{Ω}$. Add series resistances: $4 + 6 = 10$.

22. What is the effect of adding resistors in parallel on circuit current?

    Current increases. More parallel paths reduce total resistance.

23. Determine total voltage in series if $V_1 = 5 \text{V}$ and $V_2 = 3 \text{V}$.

    $V_{\text{eq}} = 8 \text{V}$. Series voltages add: $5 + 3 = 8$.

24. Identify the formula for current using charge and time.

    $I = \frac{Q}{t}$. Current is charge flow rate.

25. Find total current if $V = 12 \text{V}$ and $R = 6 \text{Ω}$.

    $I = 2 \text{A}$. Apply $I = \frac{V}{R} = \frac{12}{6} = 2$.

26. What is the effect of adding resistors in series on circuit current?

    Current decreases. More series resistance increases total resistance.

27. Determine total voltage in parallel if $V_1 = 10 \text{V}$ and $V_2 = 10 \text{V}$.

    $V_{\text{eq}} = 10 \text{V}$. Parallel voltages are equal across branches.

28. Find energy used in 2 hours if power is $50 \text{W}$.

    $E = 360,000 \text{J}$. $E = 50 \times 7200 = 360,000$ J.

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